This invention relates to vibrators and detector circuits for vibrating gyros, which are mounted on an automotive vehicle for controlling the attitude of the vehicle and for providing information upon the angular velocity of the vehicle for the navigation system thereof.
FIG. 19A is a schematic sectional view of a conventional vibrator of a vibrating gyro, showing the section along the mid-transversal plane thereof. FIG. 19B is a perspective view of the vibrator of FIG. 19A. A vibrator 61 includes a cylindrical vibrating body 62 made of a piezoelectric ceramic, upon the side surface of which sextipolar strip-shaped electrodes 63 through 66 are attached. The sextipolar strip-shaped electrodes 63 through 66 are separated by an equal circumferential angle from each other and extend in the longitudinal direction of the vibrating body 62. Among the electrodes 63 through 66, every second electrode, in the circumferential direction of the vibrating body 62, is coupled to each other at the ends thereof through circumferentially extending annular strips, to form the grounded electrodes 66. Among the remaining three, one is the driver electrode 63 and the other two are the feedback detector electrodes 64 and 65. The electrodes 62 through 64 are positively biased relative to the grounded electrodes 66, such that the vibrating body 62 is polarized as indicated by the arrows in FIG. 19A.
FIG. 20A is a schematic sectional view of another conventional vibrator of a vibrating gyro, showing the section along the mid-transversal plane thereof. FIG. 20B is a perspective view of the vibrator of FIG. 20A. The vibrator is disclosed, for example, in Japanese Patent Publication (Kokoku) No. 4-106410.
The vibrator 71 of FIGS. 20A and 20B includes a vibrating body 72 made of a piezoelectric ceramic and having an axially extending central through-bore 77. Three exterior electrodes 73, 74 and 75 are attached on the outer side surface of the vibrating body 72 at a substantially equal circumferential spacing. An interior electrode 76 is attached on the inner side surface of the vibrating body 72. One of the exterior electrodes 73, 74 and 75 is selected as the driver electrode while the other two are selected as feedback detector electrodes. The interior electrode 76 is grounded. If the exterior electrodes 73, 74 and 75 are negatively biased relative to the through-bore 77, the vibrating body 72 is biased radially, as indicated by the arrows in FIG. 20A.
FIG. 21 is a circuit diagram showing a conventional detector circuit for a vibrating gyro. The vibrator 81 includes a triangular prism-shaped vibrating body 82 made of a material exhibiting a constant modulus of elasticity, such as elinvar. Two driver piezoelectric members 84 and 85 and a feedback piezoelectric member 83 are attached on respective side surfaces of the vibrating body 82 by means of an electrically conductive adhesive.
The driver circuit 89 applies an AC voltage V across the driver piezoelectric member 84 through a resistor 86, and across the driver piezoelectric member 85 through a resistor 87. The output of the feedback piezoelectric member 83 is inputted to the driver circuit 89, such that a loop is formed to vibrate the vibrator 81. The vibrator 81 is thus vibrated in the direction of the Y-axis. The voltages V.sub.L and V.sub.R developed at junction points P1 and P2 between the driver piezoelectric members 84 and 85 and the resistors 86 and 87, respectively, are input to a differential amplifier 88.
The parameters of the circuit are selected in such a way that the voltages V.sub.L and V.sub.R input to the differential amplifier 88 are equalized when the vehicle, etc, upon which the circuit is mounted is not rotating. Thus, provided that the vehicle, etc, is not rotating, the output of the differential amplifier 88 vanishes. However, when the attitude of the vehicle, etc, is changing and the vibrator 81 is rotated around the Z-axis perpendicular to the surface of the drawing in FIG. 21, a vibration in the direction of the X-axis is developed in the vibrating body 82 due to the Coriolis force, and hence a difference is developed between the voltages V.sub.L and the V.sub.R developed at the junction points P1 and P2. The output of the differential amplifier 88, which is proportional to the difference between the voltages V.sub.L and V.sub.R, indicates the angular velocity of the rotation of the vibrating body 82.
Next, the principle of the detection of the angular velocity by means of the arrangement of FIG. 21 is described by reference to FIGS. 22A through 22D.
FIG. 22A is a schematic circuit diagram showing the equivalent electrical connections of the driver piezoelectric members 84 and 85 of FIG. 21. As shown in FIG. 22A, the driver piezoelectric members 84 and 85 are coupled across the driver circuit 89 through resistors 86 and 87, respectively. Voltages V.sub.L and V.sub.R are thus applied across the driver piezoelectric members 84 and 85 when the driver circuit 89 applies an AC voltage V across the driver piezoelectric members 84 and 85 through the resistors 86 and 87, respectively. Thus, as shown in FIG. 22B, the driver piezoelectric members 84 and 85 develop forces F.sub.L and F.sub.R perpendicular to the respective main surfaces. These forces F.sub.L and F.sub.R are equal to A.V.sub.L and A.V.sub.R, respectively, where A represents the force factor of the driver piezoelectric members 84 and 85. Thus, if the unit vectors along the X-axis and Y-axis are represented by i and j, respectively, the forces FL and FR are given by the following equations: EQU F.sub.L =A.V.sub.L. cos30.degree. . i-A . V.sub.L . sin30.degree. . j EQU F.sub.R =-A . V.sub.R . cos30.degree. . i-A . V.sub.R . sin30.degree. . j . . . (1)
The vibrator 81 is driven by the resultant of the two forces F.sub.L and F.sub.R at a velocity v.sub.Y in the direction of the Y-axis. Assume here that the vibrator 81 is rotated at an angular velocity .OMEGA. as shown in FIG. 22C. Then, a Coriolis force acting in the direction of X-axis is developed. If the equivalent mass of the vibrating body 82 is represented by m, the Coriolis force Fc is equal to: EQU Fc=2 . m . .OMEGA. . v.sub.Y . i . . . (2)
Due to the forces F.sub.L and F.sub.R developed in the driver piezoelectric members 84 and 85 and the Coriolis force Fc, the vibrator 81 vibrates at the velocities v.sub.X and v.sub.Y in the X- and Y-axis, respectively, such that a reaction Fz is developed in the vibrator 81. If the mechanical impedances of the vibrator 81 are denoted by Z.sub.X and Z.sub.Y, respectively, the reaction F.sub.Z is given by the following equation: EQU F.sub.z =-Z.sub.x . v.sub.x . i-Z.sub.Y . v.sub.y . j . . . (3)
Further, the velocity v.sub.Y of the vibrator 81 generates a voltage V.sub.B in the feedback piezoelectric member 83. In its turn, this voltage V.sub.B develops a force F.sub.B which is given by: EQU F.sub.B =A . V.sub.B . j . . . (4)
Since the forces F.sub.L and F.sub.R developed in the driver piezoelectric members 84 and 85, the Coriolis force Fc, the reaction F.sub.Z developed in the vibrator 81, and the force F.sub.B generated in the feedback piezoelectric member 83 are balanced, the sum of these forces vanishes: EQU 0=F.sub.L +F.sub.R +F.sub.c +F.sub.z +F.sub.B . . . ( 5)
The X- and Y-components of the right-hand side of equation (5) must also vanish. Thus, the following equations are obtained: EQU 0=A . cos30 .degree. . (V.sub.L -V.sub.R)+2m . v.sub.Y . .OMEGA.-Z.sub.X . v.sub.X EQU 0=A . sin30 .degree. . (V.sub.L +V.sub.R)-Z.sub.Y . v.sub.Y +A . V.sub.B . . . ( 6)
Thus, the angular velocity .OMEGA. is given by: ##EQU1##
On the other hand, if the admittance of the resistors 86 and 87 are represented by Y.sub.R, the current I.sub.L and I.sub.R flowing through the driver piezoelectric members 84 and 85 are given by: EQU I.sub.L =Y.sub.R . (V-V.sub.L) EQU I.sub.R =Y.sub.R . (V-V.sub.R) . . . (8)
Further, if the damping admittance of the driver piezoelectric members 84 and 85 is represented by Y, and the vibrating velocities of the driver piezoelectric members 84 and 85 in the direction perpendicular to the main surfaces thereof are represented by v.sub.L and v.sub.R, respectively, the above currents I.sub.L and I.sub.R are given by: EQU I.sub.L =A . v.sub.L +Y . V.sub.L EQU I.sub.R =A . v.sub.R +Y . V.sub.R . . . ( 9)
Thus, from equations (8) and (9), the following equations are obtained: EQU V.sub.L . (Y+Y.sub.R)=-(A . v.sub.L +Y.sub.R . V) . . . (10) EQU V.sub.R . (Y+Y.sub.R)=-(A . v.sub.R -Y.sub.R . V) . . . (11)
FIG. 22D shows the relationship between the velocities v.sub.L and v.sub.R and the velocities v.sub.X and v.sub.Y by means of a vector diagram, where the vx and vy are the X- and Y-components of the sum of velocities v.sub.L and v.sub.R. Using the unit vectors i and j, the X- and Y-components of the velocities vL and vR are represented by: EQU v.sub.L =v.sub.l . cos30.degree. . i-v.sub.L . sin30.degree. . j EQU v.sub.R =v.sub.R . cos30.degree. . i-v.sub.R . sin30.degree. . j . . . (12)
Thus, the velocity components v.sub.X and v.sub.Y are given by: EQU v.sub.X =cos30.degree. . (v.sub.L -v.sub.R) EQU v.sub.Y =-sin30.degree. . (v.sub.L +v.sub.R) . . . (13)
Further, subtracting equation (11) from equation (10), the following equation is obtained: ##EQU2##
Eliminating v.sub.X from equation (7) using equation (14), the following representation for the angular velocity .OMEGA. is obtained: ##EQU3##
On the other hand, since no external current flows through the feedback piezoelectric member 83, the relation EQU 0=A . v.sub.Y -Y . V.sub.B
holds, such that the following equation is obtained: EQU v.sub.Y =Y . V.sub.B /A . . . (16)
Adding equations (10) and (11) together yields: ##EQU4##
Further, from equations (16) and (17), the following equation is obtained: EQU (V.sub.L +V.sub.R)=(Y . V.sub.B -2 . sin30.degree. . Y.sub.R . V)/(sin30.degree. . (Y+Y.sub.R)) . . . (18)
Furthermore, substituting equation (18) in equation (15), the following equation is obtained: ##EQU5##
Since the variation of the denominator of the above equation (19) due to the Coriolis force F.sub.c is negligibly small, the angular velocity .OMEGA. is proportional to the voltage difference (V.sub.L -V.sub.R). Thus, the output of the differential amplifier 88, which is proportional to the difference of the voltages V.sub.L and V.sub.R at the junction points P1 and P2 between the resistors 86 and 87 and the driver piezoelectric members 84 and 85, represents the angular velocity .OMEGA. of the vibrator 81 around the Z-axis.
The above conventional vibrators and detector circuit for the vibrating gyro, however, suffer from respective disadvantages.
Namely, in the case of the vibrator 61 of FIG. 19, at least six strip-shaped electrodes 63 through 66 separated by an equal circumferential angle from each other must be formed on the side surface of the vibrating body 62, and every second electrodes 66 thereof must be coupled to each other at the two ends thereof to form the grounded electrodes. The structure of the vibrator 61 is thus complicated.
Further, to form the sextipolar strip-shaped electrodes spaced by an equal circumferential angle, the vibrating body 62 must exhibit the form of an exact cylinder. This requires a precise machining of the vibrating body 62, and raises the production cost. Furthermore, since the number of the electrodes is large, the number of conductors associated therewith becomes also large. Thus the associated circuit is prone to failure and the reliability is reduced.
In the case of the vibrator 71 of FIG. 20, the through-bore 77 is machined through the vibrating body 72 and then the whole inner side surface of the vibrating body 72 is covered with the interior electrode 76. The production steps are thus complicated and a high cost is incurred. Furthermore since the number of the electrodes is large, the number of conductors associated therewith becomes also large. Thus the associated circuit is prone to failure and the reliability is reduced.
In the case of the detector circuit for a vibrating gyro of FIG. 21, the angular velocity .omega. is calculated using the principle as expressed by the above equation (19), which includes the terminals involving the force factor A of the driver piezoelectric members 84 and 85, the damping admittance Y and the admittance Y.sub.R of the resistors. The change in the ambient temperature or the secular change accompanying a long service period of the components may induce variations in the force factor A, the damping admittance Y and the admittance of the resistors Y.sub.R. The accuracy of the detection of the angular velocity .OMEGA. is thus deteriorated. The temperature compensation of these parameters, on the other hand, is complicated. It is noted that the force factor A and the damping admittance Y of the piezoelectric members cannot be eliminated by selecting appropriate values of the output V.sub.B of the feedback piezoerectric member 83 and the driving voltage V of the driver circuit 89.